The demand function of a product is q = 7,000 - 50p, where p is the price. The cost function is given by C = 2,000 + 259. At what price is the break-even
Production attend?

139.65 or 25.34.

Step-by-step explanation:

The revenue function will be:

= Price × Quantity

= P × (7,000 - 50p)

= 7000p - 50p²

The coat function is given as:

C = 2,000 + 25q

C = 2000 + 25(7000 - 50p)

C = 2000 + 175000 - 1250p

C = 177000 - 1250p

Then, we'll equate the revenue function to the cost function. This will be:

7000p - 50p² = 177000 - 1250p

-50p² + 7000p + 1250p - 177000 = 0

-50p² + 8250p - 177000 = 0

Divide through by -50

p² - 165 + 3540 = 0

Solving to get the value of P will then give us 139.65 or 25.34.

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."